Presented at the 16th International Cryocooler Conference, held May 17-20, 2008 in Atlanta, Georgia.Theoretical modeling of thermodynamic performance plays an important role in the design and development of pulse tube cryocoolers. In the present work, a thermodynamic model of a GMtype double-inlet pulse tube cryocooler has been developed. It includes calculation of ideal refrigeration power, various losses, and hence net refrigeration power. An experimental setup was designed and fabricated to carry out experimental investigations on the GM-type double-inlet pulse tube cryocooler. Experiments were conducted, and the results obtained were used for comparison with the isothermal model developed in the present work. The effect of orifice valve opening, double-inlet valve opening, and frequency on the performance of cryocooler was studied in terms of net refrigeration power and no-load temperature

Atrey, M. D.

Desai, K. P.

Desai, S.

Naik, H. B.

Scholarly Materials And Research @ Georgia Tech

77Theoretical and Experimental Investigationof 30K Single Stage GM-TypePulse Tube Cryocooler* ME Dept., C. K. Pithawala College of Eng.  ¶Surat, India+ ME Dept., S. V. N. I. T.,  ¶Surat, India¶# ¶ME Dept., Indian Institute of Technology  ¶Bombay, IndiaABSTRACTTheoretical modeling of thermodynamic performance plays an important role in the designand development of pulse tube cryocoolers.  In the present work, a thermodynamic model of a GM-type double-inlet pulse tube cryocooler has been developed.  It includes calculation of ideal refrig-eration power, various losses, and hence net refrigeration power.  An experimental setup was de-signed and fabricated to carry out experimental investigations on the GM-type double-inlet pulsetube cryocooler. Experiments were conducted, and the results obtained were used for comparisonwith the isothermal model developed in the present work. The effect of orifice valve opening,double-inlet valve opening, and frequency on the performance of cryocooler was studied in termsof net refrigeration power and no-load temperature.NOMENCLATURES. Desai*, K. P. Desai+ H. B. Naik+ and M. D. Atrey#Figure 1. Schematic diagram of double-inlet pulse tube cryocooler: 0 - Orifice, 1 - Hotend heatexchanger, 2 - Pulse tube, 3 - Coldend heat exchanger, 4 - Regenerator, 5 - Distribution valve, 6 - Reservoir,7 - Double Inlet valve, HP - High pressure, LP - Low pressure.INTRODUCTIONApplications of pulse tube cryocoolers are increasing day by day. This includes cooling ofinfrared sensors, low noise amplifiers, MRI, SQUIDS, small capacity nitrogen liquefiers, etc. Theo-retical modeling of the pulse tube cryocooler plays an important role in its design and development.The model should be simple and clear in revealing the essentials of internal physical processes andreliable in predicting the performance of pulse tube cryocoolers.The first remarkable work in this direction was reported by Storch et al. [1] and Radebaughet al. [2].  The model developed by them describes the internal processes of a Stirling-type orificepulse tube (OPT) cryocooler using enthalpy flow analysis and investigated the performance forvarious operating parameters. Wang et al. [3] proposed a numerical model using conservation ofenergy, momentum, and continuity for performance prediction of an OPT cryocooler.  Ravex et al. [4]developed an algorithm based on the wall heat pumping effect and enthalpy flow to calculate thedominant cooling processes in both orifice and double-inlet pulse tube cryocoolers. Zhu et al. [5]proposed an isothermal model for a pulse tube cryocooler.  Liang et al. [6] has discussed the ther-modynamic non-symmetry effect. They derived a mathematical formulation considering orificeand double-inlet valves as impedance devices.  Zhu et al. [7] has developed an improved numericalmodel for simulation of the oscillating fluid flow of orifice and double-inlet pulse tube cryocoolersbased on conservation of mass, momentum, and energy. The governing equations include the pres-sure gradient, inertia, viscous, and convection terms.  Atrey et al. [8] applied this model to carry outcyclic simulations of Stirling-type orifice pulse tube cryocoolers including the losses.In a double-inlet GM-type pulse tube cryocooler, a bypass tube connects a pressure-wave gen-erator, i.e. the GM distribution valve, to the hot end of the pulse tube (see Fig. 1). The bypassreduces the mass flow rate in the regenerator, which reduces the irreversibility of the system, therebyimproving the performance.  Several comparative experiments have verified that the addition of adouble-inlet valve can lower the no-load temperature and increase the refrigeration power of apulse tube cryocooler.  Desai et al. [9] developed a theoretical model for a GM-type orifice pulsetube refrigerator based on a second-order isothermal model developed by Atrey et al [8].  FurtherInvestigation on orifice pulse tube refrigerators was carried out by Desai et al. [10].In the present work, the earlier theoretical models for orifice pulse tube cryocoolers are ex-tended to a double-inlet pulse tube cryocooler followed by experimental investigations. The effectsof various operating parameters like, frequency, orifice opening, double-inlet opening, etc. on theperformance of system are studied.MODEL DESCRIPTIONThe isothermal model for a Stirling-type orifice pulse tube cryocooler has been developed byZhu et al. [5] and extended by Atrey et al. [8] and Desai et al. [9].  It is further modified in thepresent work for a GM-type double-inlet pulse tube cryocooler as presented here.A schematic diagram of a double-inlet pulse tube cryocooler is shown in Figure 1. The pulsetube can be divided into three parts: the portion of gas in the cold region of the pulse tube that flowsfrom the regenerator into the pulse tube and expands to give out work is defined as Gas III.  Theportion of the gas that flows from the orifice into the pulse tube from the reservoir or vice versa isdefined as Gas I.  And, the gas in the central portion of the pulse tube, which never flows out of the78 GM-TYPE COOLERS FOR 4-30 K GROUND APPLICATIONSFigure 2. A typical trapezoidal waveform.pulse tube and acts similar to a displacer of split Stirling cryocooler, is defined as Gas II.  The otherassumptions made for the analysis include:1. Working gas is ideal gas2. The variation of pressure is trapezoidal as shown in Fig. 2.3. The pressure in the system remains uniform at any instant in time4. Gas I & III are isothermal and gas II is adiabatic.The governing equations are defined below, starting with the pressure variation, which is givenby Eq (1) using the time nomenclature indicated in Fig. 2:(1)Mass flow rate at the orifice is given by Eq (2) where P6 is the reservoir pressure:(2)Mass flow rate at the double-inlet valve is given by Eq (3):(3)Pressure in the orifice reservoir (P6 ) is given by Eq (4):79INVESTIGATION OF 30 K 1-STAGE GM-TYPE PULSE TUBE(4)Mass flow rate at section 1 is calculated by Eq (5):(5)Mass of Gas I is given by Eq (6):(6)where, mI0 can be obtained by ensuring (mI)min = 0.The volume of Gas I is given by Eq (7):(7)Volume of Gas II is calculated by Eq (8):(8)Volume of Gas III is calculated by Eq (9):(9)where, CII0 can be obtained from (VIII))min = 0.Eq (10) gives Gross Refrigeration Power:(10)The effect of various losses is significant on the net refrigeration power obtained from thepulse tube cryocooler. The method of calculating such losses in the case of Stirling cryocoolers iswell explained by Atrey et al. [11].Heat losses due to regenerator ineffectiveness, temperature swing, pressure drop and solidconduction loss are calculated as per Atrey et al. [11].  The net refrigeration power is calculated bysubtracting all the losses from the gross refrigeration power as given in Eq (11).(11)Many researchers have used a sinusoidal pressure wave form for such investigations, which isessentially a feature of a Stirling-type cryocooler.  Figure 2, which was plotted for 14 bar averagepressure, gives the nature of the wave form used in the present work. The model is solved usingMATLAB.DESIGN OF GM PULSE TUBE CRYOCOOLERThe model has been used to design a 100¶W capacity GM-type double-inlet pulse tube cryo-cooler having a U-tube configuration, operating at 80 K temperature, 14 bar average pressure, and1.75 Hz frequency.  The design and operating parameters are listed in Table 1, while the differentlosses calculated using the theoretical model are shown in Table 2.Table 1.  Design and operating parameters. Table 2.  Losses predicted by model.80 GM-TYPE COOLERS FOR 4-30 K GROUND APPLICATIONSThe refrigeration capacity of a cryocooler decreases because of losses such as the loss due toregenerator ineffectiveness, temperature swing, regenerator pressure drop, solid heat conductionetc.  If the effects of all individual losses identified separately are combined, as they are in the realsituation, then the net refrigerating power is substantially reduced from that pertaining to the idealcase. The loss analysis of a cryocooler is very important to estimate its efficiency and performance.The amount of gas that passes through the regenerator is quite large and consequently the loadon the regenerator is also large. Hence, the regenerator is a critical component that influences theperformance of a pulse tube refrigerator, and the regenerator efficiency is critical to its overallthermodynamic performance. The regenerator performance varies with different mesh structuresused and also with the properties of the mesh matrix material. Regenerator ineffectiveness causesthe incoming gas to be cooled to a slightly higher temperature than with an ideal regenerator, therebycausing loss of refrigeration power.Temperature swing loss accounts for the temperature changes in the matrix of the regeneratorduring the cycle. It is the heat taken up by the matrix due to its finite heat capacity. The drop intemperature of the regenerator matrix is calculated along the length of the regenerator.Due to pressure drop in the regenerator and other parts, the actual pressure in the pulse tubewill be lower than the supply pressure. During the expansion process, the gas can’t be expanded inthe pulse tube to the lowest possible pressure for the same reason. This results in a reduction of P-Varea (of gas III), and hence a reduction of the refrigeration power. The pressure drop depends onflow acceleration and core friction.  This loss is estimated based on the viscosity of the gas, gasdensity, mass velocity, Reynolds’ number, and friction factor. This is a major loss among all theother types of losses.Solid conduction loss is due to heat conduction from high temperature regions to low tempera-ture regions. It occurs down the length of the pulse tube, down the regenerator tube liner, and downthe length of the regenerator matrix. These losses also reduce the net refrigeration power and can becalculated from basic heat transfer equations.EXPERIMENTAL INVESTIGATIONA double-inlet GM-type pulse tube cryocooler was developed using the above mentioned de-sign procedure. The unit was fabricated and instrumented to carry out experimental investigations.A Leybold 6 kW helium compressor was used for the experiments, together with a rotary valvedeveloped to deliver the pressure pulse. The dimensions of the experimental setup are listed inTable 1.Results and DiscussionThe computed movements of the interfaces between the three gas regions (I, II and III) in thedouble-inlet pulse tube over one cycle are shown in Figure 3.  This gives some idea about the gasesFigure 3.  Gas interface motion over one cycle.81INVESTIGATION OF 30 K 1-STAGE GM-TYPE PULSE TUBEFigure 5.  Cooldown curve.Figure 4.  Recorded pressure waveform.that are undergoing compression and expansion over a cycle.  In the double-inlet mode, a bypass isintroduced between the distribution valve and the hot end of the pulse tube through a double-inletvalve. The introduction of a double-inlet valve reduces the gas III entering the pulse tube at the coldend. This reduces the flow of gas through the regenerator, which reduces irreversibility in the sys-tem. However the refrigerating effect per unit mass of gas increases, thereby contributing to im-proved performance for a pulse tube cryocooler with a double-inlet bypass.The pressure waveforms recorded at the warm end of the regenerator and pulse tube are shownin Figure 4.  It can be seen from the figure that the pressure at the hot end of the pulse tube is lowerthan that at the hot end of regenerator due to a drop in pressure. It was found experimentally that thesteady-state pressure ratio remains around 1.9 to 2 for different average pressures and frequencies.The no-load temperatures measured at the cold end of the pulse tube are shown in Figure 5 fordifferent operating pressures. The coldend temperature decreases linearly with time and then be-comes steady.  The lowest no-load temperature of 28 K was recorded for an average pressure of12 bar with an operating frequency of 1.7 Hz. As the average pressure increases, the compressionheat and friction heat will also increase, resulting in lower performance at 14 bar and 16 bar averagepressure.  The coldend no-load temperature reached 30 K in 30 minutes.The net refrigeration power measured at the cold end is shown in Figure 6 for various averagepressures. Refrigeration power increases with increasing coldend temperature. A net refrigeration82 GM-TYPE COOLERS FOR 4-30 K GROUND APPLICATIONSFigure 6.  Net refrigeration power at various average pressure.Figure 7.  Theoretical and experimental results for net refrigeration power.power of 20 W was measured at 56 K with an operating frequency of 1.5 Hz.A comparison of experimental and theoretical results for net refrigeration power versus coldend temperature is shown in Figure 7.  Each curve used the operating frequency that maximized itsperformance. A net refrigeration power of 37 W was measured at 80 K with 16 bar average pressureand an operating frequency of 1.5 Hz.  The theoretical model, which used the actual recordedpressure waveform as an input, predicts 99 W of net refrigeration power at 80 K for the sameoperating conditions. The difference between the theoretical and experimental results is due to thefact that the theoretical model does not calculate other losses viz. shuttle heat loss, pumping loss,DC flow heat loss, and unaccounted losses.Generally, GM-type pulse tube cryocoolers are operated at low frequencies i.e. in the range of1 Hz to 5 Hz. For a particular orifice and double-inlet opening there exist an optimum operatingfrequency for which the no-load temperature is minimum.  The effect of frequency on no-loadtemperature is depicted in Figure 8. The no-load temperature decreases with frequency, passesthrough a minima, and then increases with frequency. With an increase in frequency, the losses alsoincrease. This is due to the fact that, with an increase in frequency, initially the losses reduce mar-ginally, and thereafter they increase. This is because, at higher frequency, the cycle time reduces,83INVESTIGATION OF 30 K 1-STAGE GM-TYPE PULSE TUBEFigure 8. Effect of frequency on no load temperature.which in turn reduces the time available for the gas to flow in and out of the pulse tube. This resultsin higher losses. Hence, there exists an optimum frequency at which the no-load temperature isminimum.  At 12 bar average pressure, the theoretical model predicts an optimum frequency of2.7 Hz, in contrast to the experimentally recorded value of 1.7 Hz.CONCLUSIONThe proposed isothermal model is compared with experimental results. The model is useful inunderstanding the performance of double-inlet pulse tube cryocoolers through the behavior of thegas.  A lowest no-load temperature of 28 K was recorded using an average pressure of 12 bar and anoperating frequency of 1.7 Hz.  A net refrigeration power of 37 W was measured at 80 K at 16 baraverage pressure and 1.7 Hz frequency.REFERENCES1. Storch P. J. and Radebaugh R., “Development and Experimental Test of an Analytical Model of theOrifice Pulse Tube,” Adv. in Cryogenic Engineering, Vol. 33, Plenum Publishing Corp., New York(1988), p. 851.2. Radebaugh R, “A Review of Pulse Tube Refrigeration,” Adv. in Cryogenic Engineering, Vol. 35,Plenum Publishing Corp., New York (1990), p. 1191.3. Wang C. Wu P. and Chen Z., “Numerical modeling of an Orifice Pulse tube Refrigerator, “ Cryogen-ics, vol. 32, (1992), pp. 785.4. A. Ravex, P. Rolland and J. Liang, “Experimental study and modelisation of a pulse tube refrigerator,”Cryogenics, vol. 32, (1990), pp. 9.5. Zhu S. W. and Chen Z. Q., “Isothermal Model of Pulse Tube Refrigerator,” Cryogenics, vol. 34 (1994),pp. 591.6. Liang J. Ravex A. and Rolland P., “Study on Pulse Tube Refrigeration Part 1: Thermodynamic Non-symmetry Effect,” Cryocoolers 8, Plenum Press New York (1996), pp. 87.7. Zhu Y. L. Wang C. and Zhou Y., “Numerical Simulation and Experimental Verification of the Oscil-lating Flow in Pulse Tube Refrigerator,” Cryogenics, vol. 38 (1998), pp. 169.8. Atrey M. D. and Narayankhedkar K. G., “Development of Second Order Isothermal Model of OrificePulse Tube Refrigerator (OPTR) with Linear Compressor,” Proc. ICEC 18, (2000), pp.519.9. Desai K., Naik H. and Narayankhedkar K., “Theoretical Model for GM Type Orifice Pulse TubeCryocooler,” 21st IIR International Congress of Refrigeration, (2003).84 GM-TYPE COOLERS FOR 4-30 K GROUND APPLICATIONS10. Desai K. P., “Investigations on Orifice Pulse Tube Refrigerator” Ph. D. Thesis (2003).11. Atrey M.D. Bapat S.C. and Narayankhedkar K. G., “Cyclic simulation of Stirling Cryocoolers,” Cryo-genics, vol. 30, (1990), pp. 341-347.12. Desai S., Desai K. P., Naik H. B. and Atrey M. D.,  “Performance Prediction of PTR for DifferentPressure Waveforms,” Adv. in Cryogenic Engineering, Vol. 53, Amer. Institute of Physics, Melville,NY (2008), pp. 1691.13. Ravex A., Poncet J. M., Charles I. and Bleuze P., “Development of Low Frequency Pulse Tube Refrig-erator,” Adv. in Cryogenic Engineering, Vol. 43B, Plenum Publishing Corp., New York (1998), pp.1957.14. Koh D. Y., Park S. J., Lee S. J., Yeom H. K., Hong Y. J. and Jeong S. K., “An Experimental Investiga-tion of the Pulse Tube Refrigerator,” Cryocoolers 9, Plenum Press, New York (1997), pp. 239.15. Thummes G. Giebeler F. and Haiden C., “Effect of Pressure Wave Form on Pulse Tube RefrigeratorPerformance,” Cryocoolers 8, Plenum Press, New York, (1995), pp. 383.85INVESTIGATION OF 30 K 1-STAGE GM-TYPE PULSE TUBE

Theoretical and Experimental Investigation of 30 K Single Stage GM-Type Pulse Tube Cryocooler

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Theoretical and Experimental Investigation of 30 K Single Stage GM-Type Pulse Tube Cryocooler

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